Causal Reasoning that Derives Conditional Possibility Distributions of Arbitrary Nodes in a Hierarchical Causal Network

Abstract

This paper addresses a reasoning in a hierarchical causal network that derives conditional possibility distributions of arbitrarily chosen nodes, when some other nodes are instantiated. The study is a step toward a more general reasoning that works on a directed acyclic graph in a possibilistic way. However, it is ahead of some studies done before which dealt with the inverse problem of causation using Possibility Theory, because the causal reasoning in this study includes the inverse problem.
First, the paper introduces Causation Event expressing an event that “a cause actually causes an effect”, and Conditional Causal Possibility meaning conditional possibility that a causation event occurs when its cause is observed. Then, it discusses some characteristics of conditional causal possibilities and relations with conventional conditional possibilities. It also applies them to causation analysis which is a problem to derive conditional possibility distributions of arbitrarily chosen nodes in a hierarchical causal network. Finally, it shows a numerical example and discusses its results.